Three mathematical models based on approximate surface integral equations for electromagnetic analysis of scalar wave scattering from thin extended target are considered. Such models include different systems of the second kind singular integral equations determined on the target median. The effective algorithm for direct (without preliminary regularization) numerical solution of the systems is based on the special quadrature formulae for singular integrals. Verification of the mathematical models and their comparison is performed in the case of penetrable cylindrical shell in homogeneous non-magnetic medium.
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